Direct and Photon-Assisted Tunneling in Resonant-Cavity Quantum-Well Light-Emitting Transistors

Direct and photon-assisted tunneling in resonant-cavity quantum-well light-emitting transistors

Cite as: J. Appl. Phys. 124, 234501 (2018); https://doi.org/10.1063/1.5042418 Submitted: 31 May 2018 . Accepted: 20 October 2018 . Published Online: 18 December 2018

Junyi Qiu , Curtis Y. Wang, Milton Feng, and N. Holonyak

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J. Appl. Phys. 124, 234501 (2018); https://doi.org/10.1063/1.5042418 124, 234501

Direct and photon-assisted tunneling in resonant-cavity quantum-well light-emitting transistors Junyi Qiu, Curtis Y. Wang, Milton Feng, and N. Holonyak, Jr. Department of Electrical and Computer Engineering, Micro and Nanotechnology Laboratory, University of Illinois at Urbana-Champaign, Champaign, Illinois 61801, USA (Received 31 May 2018; accepted 20 October 2018; published online 18 December 2018) Tunneling in a transistor is a critical quantum process toward the next-generation, energy-efﬁcient, high-speed data transfer for both electrical and optical communications. In this work, resonant- cavity quantum-well light-emitting transistors with tunneling collector junctions are designed and fabricated. Three distinctive tunneling mechanisms are clearly identiﬁed by the transistor optical output family curves, namely, electron direct tunneling (DT) from collector to base, electron DT from base to collector, and intra-cavity photon-assisted electron tunneling from base to collector. The device operations under both direct and photon-assisted tunneling are explained in detail by the intra-cavity quantum transition of electron-hole pair to photon dynamics. The tunnel junction and the corresponding carrier tunneling injection suggest the possibility of utilizing tunneling to achieve high-speed optoelectronics operations. Published by AIP Publishing. https://doi.org/10.1063/1.5042418

I. INTRODUCTION insertion of a double quantum-well in the base and a 15 nm The invention of the transistor by Bardeen and Brattain1 In0.05Ga0.95As layer between the base and the collector as the marks the beginning of transistor integrated circuits and tunneling region. In addition to the transistor base QWs providing the electron-hole (e-h) recombination and photon serves as the basis for an information revolution. The transistor establishes the spontaneous electron-hole recombination, generation, the collector junction incoherent-tunneling intro- supporting signal amplification and switching by voltage duces additional carrier injection mechanisms and is shown to have a significant effect on the device operation; electrons control of the emitter and the collector junctions with minority carrier injection, recombination, and collection. Utilizing tunneling from base to collector can be shown to increase the a direct bandgap compound semiconductor material, hetero- base QW photon generation because of the associated hole creation; at higher bias, ICPAT dominates and a transition interfaces, and quantum-wells (QWs), the light-emitting tran- sistor2,3 and the transistor laser4,5 introduce stimulated from direct tunneling to inelastic tunneling is observed. electron-hole recombination to coherent photon generation in Detailed DT and ICPAT tunneling mechanisms are revealed in the optical (L–V) family curves in contrast to the transistor the base and result in a broad spectrum of new functionali- I–V ties. Contrary to light-emitting diodes (LEDs) and diode collector current ( ) outputs. lasers (DLs), where the active region is nearly intrinsic, the This work demonstrates the use of a collector tunnel junction in transistors to control emitter carrier injection, fast quantum-well transistor’s base is thin and heavily doped to 1019 cm3, resulting in a short recombination lifetime and base transport, and QW recombination in optoelectronic thus inherently higher optical modulation bandwidth. devices, which may provide a much faster modulation method in comparison with the conventional current modula- Experimentally, a light-emitting transistor with a modulation tion of LEDs, and DLs which rely on slow diffusion for bandwidth f–3dB = 7 GHz corresponding to a radiative recombination lifetime of 23 ps has been reported.6,7 Also, a tran- carrier supply. sistor laser with a resonance-free 20 GHz bandwidth and a carrier recombination lifetime as low as 29 ps has been con- firmed.8 Furthermore, we have realized intra-cavity photon- II. DEVICE FABRICATION AND MEASUREMENT SETUP assisted tunneling (ICPAT) providing the coherent photon absorption to electron-hole tunneling generation at the tran- The RCLET’s structure and band diagram are drawn – sistor collector junction.9 14 This coherent-ICPAT process schematically in Fig. 1. The basic structure is an n-InGaP/ suggests that the collector region can be used as a built-in p+-GaAs/n+-GaAs heterojunction bipolar transistor (HBT): electro-absorption modulator (EAM) allowing direct voltage- the emitter is a 53 nm In0.49Ga0.51P layer with a doping modulation on the semiconductor laser. of 1017 cm3; the base region is GaAs with a doping of 19 20 –3 Different than the previous work on coherent-ICPAT 10 –10 cm and an undoped In0.2Ga0.8As double QWs; – in transistor lasers,9 16 this work focuses on the physical the collector is GaAs with a doping of ∼1019 cm3;an mechanisms of direct tunneling (DT) and incoherent-ICPAT In0.05Ga0.95As layer of 15 nm thickness is inserted between and their interactions observed in the unique optical family the base and the collector to serve as the tunneling region. characteristics of resonant-cavity light-emitting transistors The resonant cavity is realized with a 4-pair distributed (RCLETs). The new design of RCLETs includes the Bragg reflector (DBR) (12%–90% AlGaAs) on the top and a

0021-8979/2018/124(23)/234501/6/$30.00 124, 234501-1 Published by AIP Publishing. 234501-2 Qiu et al. J. Appl. Phys. 124, 234501 (2018)

FIG. 1. Resonant-cavity quantum-well light-emitting transistor (RCLET) structure (left) and band diagram (right) showing the reduced gap tunnel junction placed at the base-collector junction and the additional hole supply due to base-to-collector electron direct tunneling under collector reverse bias.

36-pair DBR on the bottom. The device fabrication proce- the existence of tunneling behavior. As shown in Fig. 3(a), dure can be found in previous publications.2,3 a negative differential resistance region appears in the diode Figure 2 shows (a) the fabricated device under SEM and I–V curve, which is the signature of a tunnel diode.14 The (b) the optical emission viewed with an IR camera under an device band diagram is simulated with Sentaurus TCAD and optical microscope. The device has a planar contact layout plotted in Fig. 3(b) for reference. When the collector junction for potential high-speed applications and can be probed with is reverse biased (VBC , 0 V), electrons tunnel from the base two sets of ground-signal-ground (GSG) probes following valence band to the collector conduction band; at a small BC the conventional transistor common-emitter setup. A lensed junction forward bias (VBC . 0 V), electrons tunnel from the multimode fiber (core diameter 50 μm) is used to couple the collector conduction band to the base valence band; under spontaneous light output from the RCLET emission area, and higher forward bias (VBC . 0 V), electrons diffuse from the the spectrum is plotted in a linear scale in Fig. 2(c) with a collector to the base. The C-to-B tunnel current increases peak wavelength at 969.8 nm and a full-width half-maximum with the junction bias until the collector Fermi-level aligns (FWHM) of 10.6 nm. Due to the small light emission area, with the base valence band, at which point a peak current the lack of light output directionality, and the limited accep- (IP) of 2.35 mA is recorded at a peak voltage (VP) of 0.14 V; tance angle of fiber, we could only collect a few microwatts further increasing the junction bias will reduce the amount of of power, which is a major limiting factor at this stage. available equal-energy states in the base valence band and reduce the tunnel current, giving rise to the negative differential resistance. The simulated band diagram shows that the I –V III. BASE-COLLECTOR TUNNEL DIODE BC BC separation between the base valence band and the collector CHARACTERISTICS Fermi-level is 0.074 eV, which is smaller than the measured The diode IBC–VBC characteristics of the base-collector peak voltage; this is likely due to the non-negligible series (BC) junction are measured at room temperature to confirm resistance introduced by contact resistance and the device

FIG. 2. (a) SEM image of the ﬁnished RCLET device; the contacts are placed on the top with emitter metal (EM), base metal (BM), and collector metal (CM). (b) Microscopic top view of the device under testing; light emission (∼980 nm) can be observed with an IR camera; a lensed multimode ﬁber is used to couple the light output; only a fraction of the total power can be col- lected due to the small emission area and the lack of light output directionality. (c) RCLET emission spectrum measured at a bias of VBE ¼ 1:5Vand VCB ¼ 0:5 V; the peak emission is at 969.8 nm with a full-width half- maximum of 10.6 nm. 234501-3 Qiu et al. J. Appl. Phys. 124, 234501 (2018)

FIG. 3. (a) Room-temperature base-collector junction tunnel diode I–V measurement showing the negative differential resistance region (red) as a result of direct tunneling, which is consistent with the behavior of tunnel diodes.14 The emitter-base voltage is kept at zero (shorted) during the measurement. The current and voltage polarities are chosen in accordance with the tunnel diode convention. A peak current of 2.35 mA is recorded at a peak voltage of 0.14 V; the forward voltage is 0.69 V; the valley current and voltage cannot be easily determined due to the fluctuations in the negative differential region; the purple dotted line shows the fitting of the exponential diode I–V curve. (b) RCLET band diagram simulation done with Sentaurus TCAD to show the energy level alignment in the base-collector tunnel junction; at equilibrium, the base valence band edge is estimated to be 0.074 eV above the Fermi-level, and the collector conduction band edge is 0.107 eV below the Fermi-level. However, the measured peak voltage VP in Fig. 3(a) is twice the expected value (the simulated potential difference between the base valence band and the collector Fermi-level), probably due to the non-negligible series resistance introduced by the contact resistance and extrinsic region. extrinsic region. Note that the fluctuations in the negative dif- The simulated band diagram in Fig. 3(b) suggests that ferential resistance region are due to the oscillation caused by the transistor already pinches-off at zero BC junction bias; the measurement instrument’s control loop, and thus we were thus, the RCLET is fully functional at VCB ¼ 0V. In not able to obtain a smooth curve to accurately determine the Fig. 4(ii), when the BE junction is not turned on yet valley current and voltage. (0, VBE , 1 V), the base current plot is exactly the same as the BC diode curve because all the carrier movements in the base come from the BC junction, and IB ¼ 0 when IV. TRANSISTOR ELECTRICAL IC–VCB AND OPTICAL VCB ¼ 0; when the BE junction turns on with VBE . 1V, L–VCB FAMILY CURVES the base sees an additional electron injection from the BE The BC diode characteristics in Fig. 3(a) are redrawn with junction; thus, the base recombination will increase, causing inverted current-voltage polarities as shown in Fig. 4(i) for the base to draw more positive charges from the base termi- easy comparison to the RCLET collector current outputs. The nal and the base current increases regardless of VCB bias, . ¼ transistor base current IB, collector IC–VCB, and the correspond- and IB 0 when VCB 0. In Fig. 4(iv), when the BC junc- , ing optical L–VCB family of curves are measured and plotted in tion is forward biased at VCB 0 V, holes will leak from the Figs. 4(ii)–4(iv). Different from the typical common-emitter transistor base to collector and thus reduce the QW photon fl – bipolar transistor’s collector output IC–VCE family curves, i.e., generation, which is re ected in the optical L VCB family sweeping VCE at constant IB levels, the RCLET is characterized curves by the reduced optical output power in both regions A ¼ by sweeping VCB at constant VBE levels in order to reveal and B compared with when VCB 0 V. However, when the clearly the voltage-controlled BC junction tunneling output BC junction is reverse biased at VCB . 0 V and we allow behavior. Figures 4(ii)–4(iv) illustrate the transistor operation electrons to tunnel from base to collector, the optical output with the collector junction bias going from forward ( 1 , starts to increase despite the constant base hole supply; at the ¼ VCB , 0 V) to reverse (0 , VCB , 3 V) and the emitter junc- extreme case when VBE 0 V, i.e., zero base hole supply, tion under forward bias (0 , VBE , 2V, ΔVBE ¼ 0:25 V). there is still light output except at a higher VCB bias. This Four different transistor operation regions are shown in phenomenon is explained in Sec. V and can be attributed Fig. 4(iii) collector IC–VCB and 4(iv) optical L–VCB. to the hole (empty states) creation in the base due to elec- Specifically, one diffusion and three tunneling mechanisms trons tunneling from the base valence band to the collector are identified: (A) electron diffusion from collector to base conduction band, and thus region C represents the tunnel- and hole diffusion from base to collector under collector ing carrier injection supplying the photon generation junction strong forward bias; (B) direct electron tunneling process, which is a novel approach in contrast to the con- from collector to base under weak forward bias; (C) direct ventional carrier diffusion supply, and has the benefitof electron tunneling from base to collector under weak reverse fast modulation speed (limited by femtosecond tunneling bias; and (D) intra-cavity photon-assisted electron tunneling time) and high sensitivity (exponential tunneling I–V rela- from base to collector under strong reverse bias; the detailed tion). For example, as shown in Fig. 4(iv) L–VCB family analysis and explanations can be found in Sec. V, with the curves, it is possible to bias the device at VBE ¼ 1:75 V band diagram schematics, carrier distribution, recombination, and modulate VCB between 0 and 1 V to realize an effi- and transport corresponding to the different operating regions cient, direct-voltage, tunneling modulation on the optical (A, B, C, and D) plotted in Figs. 5–8 to explain the device output in addition to the conventional base current injec- behaviors. tion modulation. 234501-4 Qiu et al. J. Appl. Phys. 124, 234501 (2018)

FIG. 5. Band diagram corresponding to region (A) in the transistor family curves in Fig. 4 for the transistor collector junction under forward bias with 1 , VCB , 0:5 V and the emitter junction also under forward bias with 0 , VBE , 2V (ΔVBE ¼ 0:25 V). In this case, the collector Fermi-level is above the base valence band. In region (A), the collector current IC is a forward diffusion current due to the lower collector barrier conﬁnement. Minority electrons from both the emitter (Δn1) and the collector (Δn2) diffuse into the base region. The majority holes (Δp1) and (Δp2) originate from the dielectric relaxation from the base contact in response to the minority electron injection to maintain the base charge neutrality.

junction is also under forward bias with 0 , VBE , 2V (ΔVBE ¼ 0:25 V), as in region (A). The minority carrier distributions in the base (Δn1) and (Δn2) are diffused from both the emitter and the collector, respectively; the majority carrier (hole) distributions (Δp1) and (Δp2) are responding to the minority carrier electron injection via dielectric relaxation from the base contact to maintain the base charge neutrality. Thus, the collector current (IC) is equal to the sum of the collector-to-base electron diffusion current (ICn) and the FIG. 4. RCLET electrical and optical family curves measured with VCB from base-to-collector hole diffusion current (I ), both of which – Cp 1 to 3 V and VBE from 0 to 2 V. The base current (ii) follows the BC tunnel are in the opposite direction of the collector current defined diode curve (i) when VBE , 1 V and is offset by the emitter-to-base injection when VBE . 1 V. The collector current (iii) increases exponentially in the under the normal transistor forward active operation, and ICp high bias region due to BC junction tunneling. The negative slope when 0:5 , VCB , 0 V corresponds to the negative differential resistance region of the BC tunnel diode. Four operating regions (A–D) can be identified that correspond to different diffusion or tunneling mechanisms. Four band dia- grams are drawn schematically in Figs. 5–8, respectively. The optical power is measured by fiber coupling with a lensed multimode fiber, thus the low coupling efficiency.

Currently, due to RCLET’s spontaneous emission and fiber coupling setup, the received optical power level is too low for meaningful RF characterization; additionally, the fact that the fiber could only couple a fraction of the total light output means we cannot quantitatively analyze the RCLET’s internal electron-photon conversion rate or quantum efficiency. In the future, we may redesign the device layout to improve the light output directionality and extraction efficiency in order to obtain a high signal-to-noise ratio for mod- FIG. 6. Band diagram corresponding to region (B) in the family curves in ulation experiments. Fig. 4 for the transistor collector junction under forward bias with 0:5 , VCB , 0 V and the emitter junction also under forward bias with 0 , VBE , Δ ¼ : L–V 2V ( VBE 0 25 V). In this case, the collector Fermi-level is between the V. ANALYSIS ON OPTICAL CB TUNNELING base valence-band and the base Fermi-level. Electrons tunnel from collector OPERATION REGIONS to base and recombine with base holes, reducing the QW radiative recombination and light output. The tunnel current is in the opposite direction of the Figure 5 shows that the transistor base-collector junction collector current and results in the collector current reduction I ¼ , , C is under forward bias with 1 VCB 0 V and the emitter It Itunnel CtB or the negative differential resistance. 234501-5 Qiu et al. J. Appl. Phys. 124, 234501 (2018)

FIG. 8. Band diagram corresponding to region (D) in the family curves in FIG. 7. Band diagram corresponding to region (C) in the family curves in Fig. 4 for the collector under reverse bias with 0 , VCB , 3 V and the emitter- , , Fig. 4 for the transistor collector under reverse bias with 0 VCB 3V base junction under forward bias with 0 , VBE , 2V ðΔVBE ¼ 0:25 VÞ.In and the emitter under forward bias with 0 , VBE , 2V (ΔVBE ¼ 0:25 V). In this case, the collector Fermi-level is further below the base Fermi-level. this case, the collector Fermi-level is below the base Fermi-level. Electrons Electrons are direct tunneling from base to collector as well as intra-cavity tunnel from base to collector, creating additional holes in the base and thus photon-assisted tunneling (ICPAT) from base to collector. The maximum of increasing the light output. The tunnel current is in the same direction as the optical output is reached when the photon generation rate by e-h recombination collector current. The base holes (Δp2) are created by electron direct tunnel- at the QWs is equal to the photon absorption rate by ICPAT at the collector. ing from base to collector; this causes the electron accumulation (Δn2) in the When the photon generation rate is less than the photon absorption rate, the conduction band near the collector junction which increases the collector light output is reduced. Two tunnel currents exist and are both in the same direc- ¼ þ þ drift current (It DT ). Thus, IC It It DT Itunnel BtC and a DT current gain tion as the collector current. Thus, IC ¼ It þ It DT þ It ICPAT þ Itunnel BtC þ fi β ¼ þ = can be de ned as DT (It DT Itunnel BtC) Itunnel BtC. IICPAT and a new tunneling (DT + ICPAT) current gain can be defined as β ¼ þ þ þ = þ ICPAT (It DT It ICPAT Itunnel BtC IICPAT ) (Itunnel BtC IICPAT ). can be regarded as the hole leakage from the base region. Finally, the base current (IB) as seen from the terminal is collector current and the optical output reduce [the negative dif- equal to the base recombination current (IB, rec) plus ICp with ferential resistance region in Figs. 4(iii) and 4(iv)]. We express a positive current direction, because positive charges need to the electrical and optical outputs in region (B) as be injected into the base from the terminal in order to ¼ balance the hole reduction through recombination (IB, rec) and IC It1 Itunnel CtB, (3) leakage (ICp), which is indicated in Fig. 4(ii). Note that the optical output (L) is proportional to the base recombination L ¼ ηIB,rec ¼ η(IB Itunnel CtB): (4) current IB, rec, and we denote the overall conversion efficiency as η. When the collector junction forward bias decreases, the When V approaches zero (equilibrium), I will hole leakage current I is reduced; thus, both I and the CB tunnel CtB Cp C decrease due to the lack of available empty states at the base optical output will increase but I will decrease as shown in B side; thus, both I and optical outputs reach minimum and the transistor I –V and L–V family curves. We may C C CB CB recover, resulting in the negative slope region (B). express the transistor electrical and optical outputs in region When the collector Fermi-level (E ) is below the base (A) as Fn Fermi-level (EFp) under collector reverse bias, the base valence band electrons tunnel to the empty states above the collector I ¼ I I I ¼ αI I I , (1) C t Cn Cp En Cn Cp Fermi-level as shown in Fig. 7. This direct tunneling current (I )increasesI and creates additional holes (Δp , states ¼ η ¼ η tunnel BtC C 2 L IB,rec (IB ICp), (2) empty of electrons), which then drift toward the QWs for radiative recombination; therefore, the base recombination current where α denotes the base transport factor and IEn is the (IB, rec) and the light output will increase [Fig. 4(iv)]; mean- emitter-to-base electron injection current. while, the base current IB as seen by the terminal will decrease When the collector junction voltage VCB places the col- and even become negative because the base now can have an lector Fermi-level (EFn) between the base valence band (EV ) excess of positive charges due to the hole creation by collector and the base Fermi-level (EFp), the collector electrons tunnel tunneling [Fig. 4(ii)]. The excess positive charges in the base to the empty states in the base, as shown in Fig. 6. This will also lower the emitter-base junction energy barrier and results in a direct tunneling current Itunnel CtB in the opposite allow the electrons (negative charge) to be injected from the direction of IC. Since the electrons tunneling to the base will emitter via dielectric relaxation transport in order to maintain occupy the empty states in the valence band and effectively charge neutrality in the base region. Thus, the corresponding recombine with holes, the base terminal current IB will increase electrons (Δn2) will accumulate near the collector junction in response as shown in the negative differential region in and result in the additional collector drift current It DT and Fig. 4(ii); and since it is a non-radiative process which leave provide (base + QWs) recombination. Thus, the typical tran- fewer holes available for radiative recombination, both the sistor diffusion current gain β can be obtained and a new 234501-6 Qiu et al. J. Appl. Phys. 124, 234501 (2018)

β fi – direct tunneling (DT) current gain DT can be de ned. We demonstrate in the L VCB family curves (Fig. 4)three may write for region (C) tunneling processes: collector-to-base electron direct tunneling, base-to-collector electron direct tunneling, and ¼ þ þ IC It It DT Itunnel BtC, (5) base-to-collector electron intra-cavity photon-assisted tunneling, all of which are controlled by VCB. L ¼ ηIB, rec ¼ η(IB þ Itunnel BtC), (6) VI. CONCLUSION AND FUTURE WORKS I I þ I β ¼ t and β ¼ t DT tunnel BtC : (7) I DT I Resonant-cavity quantum-well light-emitting transistors B tunnel BtC with tunneling collector junctions are designed, fabricated, and analyzed. Unique transistor electrical and optical behaviors ¼ ¼ For VBE 0, the emitter diffusion current It 0 and are observed as a result of the carrier DT and ICPAT tunneling. only base-to-collector direct tunnel (DT) electrons can occur By sweeping the base-collector junction bias, the switching ≥ – at VCB 0 as shown in the collector IC VCB relation. between three tunneling mechanisms is clearly observed. Thus, Δ However, the holes ( p2) will take a longer time to diffuse to the introduction of a tunneling collector has significantly modi- the QWs for radiative recombination compared with the short fied the optical output of a light-emitting transistor. These response time of the base dielectric relaxation electron transport results support the possibility of applying tunneling modulation and the collector drifting. Thus, the additional DT collector on optoelectronic devices and utilizing the ultrafast tunneling fi drift current It DT contributes signi cantly to the total collector process to achieve high-speed operations. current TC owing to the large tunneling current gain. Hence, we need to raise VCB 1:5 V to obtain more DT electrons in ACKNOWLEDGMENTS order to achieve steady-state light output as shown in Fig. 4(iv) The authors wish to acknowledge the support of Dr. region (C) on the VBE ¼ 0 trace. Since the diffusing current Michael Gerhold of the Army Research Office (ARO) under It ¼ αIEn and IB increases with increase in VBE,thelight Grant No. W911NF-17-1-0112. They also would like to output (L) increases with increasing DT and base current IB. Figure 8 shows that the base electrons tunnel to the col- acknowledge the Pao Family fellowship. This project has lector via both DT and incoherent intra-cavity photon-assis- been partially supported by the National Science Foundation ted tunneling (ICPAT) under higher collector reverse bias. under Grant No. 1640196 and the Nanoelectronics Research Corporation (NERC), a wholly-owned subsidiary of the As the DT current increases with VCB and the base current IB Semiconductor Research Corporation (SRC), through increases with VBE, the base QW radiative recombination (photon generation) rate will increase as shown in Fig. 4(iv) Electronic-Photonic Integration Using the Transistor Laser for fi region (C). The cavity photon confinement by the top and Energy-Ef cient Computing, an SRC-NRI Nanoelectronics bottom DBR structures and the strong electric field in the Research Initiative under Research Task ID 2697.001. They collector junction provides the necessary conditions for appreciate Mr. Adam B. Auten for the low temperature setup photon-assisted tunneling for photon absorption and e-h gen- and measurement on the tunneling junction measurement. eration. Since the photon absorption rate at the collector junc- 1J. Bardeen and W. H. Brattain, Phys. Rev. 74, 230 (1948). tion by ICPAT (governed by the tunneling time) is faster 2M. Feng, N. Holonyak, Jr., and W. Hafez, Appl. Phys. Lett. 84, 151 than the photon generation rate in the base QWs (limited by (2004). the recombination lifetime), the light output reaches a 3M. Feng, N. Holonyak, Jr., and R. Chan, Appl. Phys. Lett. 84, 1952 (2004). 4 85 maximum and then decreases. The collector current output G. Walter, N. Holonyak, Jr., M. Feng, and R. Chan, Appl. Phys. Lett. , 4768 (2004). does not easily separate between the e-h generation from DT 5M. Feng, N. Holonyak, Jr., G. Walter, and R. Chan, Appl. Phys. Lett. 87, and ICPAT; however, the optical output clearly exhibits the 131103 (2005). 6 distinct difference as shown in Fig. 4(iv) region (C) for DT C. H. Wu, H. W. Then, M. Feng, N. Holonyak, Jr., and G. Walter, Appl. Phys. Lett. 94, 171101 (2009). and region (D) for ICPAT. We may write for region (D) 7G. Walter, C. H. Wu, H. W. Then, M. Feng, and N. Holonyak, Jr., Appl. Phys. Lett. 94, 231125 (2009). 8 IC ¼ It þ It DT þ It ICPAT þ Itunnel BtC þ IICPAT , (8) M. Feng, H. W. Then, N. Holonyak, Jr., G. Walter, and A. James, Appl. Phys. Lett. 95, 033509 (2009). 9A. James, J. Holonyak, Jr., M. Feng, and G. Walter, IEEE Photonics L ¼ ηIB,rec Labsorb Technol. Lett. 19, 680 (2007). 10 101 ¼ η þ þ M. K. Wu, M. Feng, and N. Holonyak, Jr., Appl. Phys. Lett. , 081102 (IB Itunnel BtC IICPAT ) Labsorb, (9) (2012). 11M. Feng, J. Qiu, C. Y. Wang, and N. Holonyak, Jr., J. Appl. Phys. 119, I þ I þ I þ I 84502 (2016). β ¼ t DT t ICPAT tunnel BtC ICPAT 12 120 ICPAT , (10) M. Feng, J. Qiu, C. Y. Wang, and N. Holonyak, Jr., J. Appl. Phys. , Itunnel BtC þ IICPAT 204501 (2016). 13C. H. Wu and C. H. Wu, in CS MANTECH Proceedings (CS MANTECH where IICPAT accounts for the electron current swept to the Conference, 2014), p. 87. 14 collector terminal due to ICPAT, It ICPAT accounts for the L. Esaki, Phys. Rev. 109, 603 (1958). dielectric relaxation transport current in response to ICPAT, 15G. E. Stillman and C. M. Wolfe, “Avalanche photodiodes,” in Infrared Detector (II), Semiconductors and Semimetals (Academic Press, 1977), and Labsorb accounts for the photon absorption due to the – fi Vol. 12, pp. 291 391. same effect, and we again de ne a new tunneling gain 16C. M. Wolfe, N. Holonyak, Jr., and G. E. Stillman, Physical Properties of β – ICPAT that accounts for both DT and ICPAT. Thus, we Semiconductors (Prentice Hall, Englewood Cliffs, NJ, 1989), pp. 219 220.